Do genetic algorithms also evolve?
In principle, yes, you can also evolve the genetic algorithm (or, in general, evolutionary algorithm), i.e. you can evolve its operations (such as the mutation and cross-over) and hyper-parameters (such as the size of the population or mutation rate). For example, you could use genetic programming to evolve the cross-over operation of a genetic algorithm. However, these genetic operators and hyper-parameters are usually designed and determined by a human and do not change during the evolution process. Nevertheless, there is a framework for evolutionary computation in which reproduction and mutation can also evolve, known as auto-constructive evolution, and there are other examples in the literature of meta-optimization methods applied to evolutionary algorithms, such as

Evolutionary principles in self-referential learning, or on learning how to learn: The meta-meta-... hook (1987, Schmidhuber's thesis)

Parallel optimization of evolutionary algorithms (1994, by T. Bäck)

Adaptive and Self-adaptive Evolutionary Computations (1995, by Peter Angeline)

Meta-Genetic Programming: Co-evolving the Operators of Variation (1998, by B. Edmonds)


More generally, the optimization of an optimization algorithm is known as meta-optimization and/or hyper-parameter optimization/tuning, so the idea of meta-optimization is not just restricted to evolutionary algorithms, but can be applied also to e.g. deep learning.